Another person de-lurking to say I've followed you from the start, its like a daily routine now to check in and see how you are all doing. (Although I've lost track of LittleEsme since she had her scare - hope she is ok). You are truly amazing, and "listening to you all share parts of your life and give each other support" makes such a difference to my day. You are a lot of things to a lot of people - even people that you don't know.
I'm sincerely hoping that this is the drink speaking, and you will be off to sleep/passing out soon only to return a little bit sheepish/embarassed tomorrow where you say sorry for scaring the hell out of us all. (And you are, because regardless of what you may think, we all do care about you - we can't help it - you are amazing, and you've let us into your life and now you are stuck with us all - the vocal and lurkers alike).
But just in case, there is more going on and it's not just the drink talking...
You are and always will be the world to your children. It is not about them being the world to you. That is what you are to them. The world, the universe, the multi-universes and everything in them.
No matter how crap you think you might be for them, or whatever it is you are telling yourself right now - you will always be their world, their piece of safety and security in this world. A world that has changed so much for them too - so the safety net is more important than ever - and there is no one, anywhere, that can replace you or give it to them in the unconditional way that you do - no one. Would you really ever chose to take that away from them? It would shape their future and their relationships with everyone they let into their lives from that day forward. Really in the grand scheme of things - is there anything more important than that safety they feel knowing you are there and you love them and that you are their world?
It is hard to start again, having to be strong for your children when your world feels like it has collapsed, but as many others have promised...it will get better. No you can't see it yet - because the hole that life has thrown you in is in the dark right now. (Whenever I've felt the way that I suspect you feel, i always imagine its like I'm in a really deep hole that I have to dig myself out of, and at/near the bottom it is just to dark to see the light. Eventually you climb out, sometimes you can find a ledge to rest on, and sometimes you exist rather than live, but eventually you see the light again) Yes - its a bloody fight and you are going to have crap days and weeks. But then the days will start feeling lighter, you'll find days where you don't have to fight so hard just to get through the day. You'll get through it and little by little, you'll find yourself again. You'll find a new way of life - sure it's not the old, but there will be new routines, new family, and new friends and before you know it you will feel like you again. Your life will get there - you just have to give yourself time and don't beat yourself up too much.